1/2p-(1/4p-4)=3/4p-4

Solution for 1/2p-(1/4p-4)=3/4p-4 equation:

1/2p-(1/4p-4)=3/4p-4

We move all terms to the left:

1/2p-(1/4p-4)-(3/4p-4)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 4p-4)!=0

p∈R


We get rid of parentheses

1/2p-1/4p-3/4p+4+4=0

We calculate fractions


4p/8p^2+(-6p-1)/8p^2+4+4=0

We add all the numbers together, and all the variables

4p/8p^2+(-6p-1)/8p^2+8=0

We multiply all the terms by the denominator


4p+(-6p-1)+8*8p^2=0

Wy multiply elements

64p^2+4p+(-6p-1)=0

We get rid of parentheses

64p^2+4p-6p-1=0

We add all the numbers together, and all the variables

64p^2-2p-1=0

a = 64; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·64·(-1)
Δ = 260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{65}}{2*64}=\frac{2-2\sqrt{65}}{128}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{65}}{2*64}=\frac{2+2\sqrt{65}}{128}
$